I think it should work with the current wording, just as it keeps working if Stern Censor leaves the game. Originally I just wanted to make it ": this and target permanent lose all non-mana abilities." but to help with memory issues I added the counter.
See Aven Mimeomancer for example.
The second ability on Stern Censor ("Permanents with Censorship counters...") is a static ability that is only present on Stern Censor itself, so it ceases to apply when Stern Censor leaves the battlefield.
It's subtle, but the way you currently have it worded and formatted, the Stern Censor has two abilities that are completely separate: One puts counters on permanents; one tells you how to treat permanents with counters on them.
Aven Mimeomancer (good find; I'd forgotten about it) has only one ability - this is easier to see if you Remove the conditional (i.e. the "if") clauses, to see what it's really doing: "At the beginning of your upkeep, you may have target creature become a 3/1 bird with flying." The conditionals just modify that.
Compare this to your activated ability, which just reads "Put a Censorship counter on target permanent." The second - separate, static - ability tells you what that means.
Fixing this is as simple as adding the "if you do" that links the text on Aven Mimeomancer together into one big block. Or just specifying activated abilities.
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